Dilations on Circular Grid

Draw

Here are Circles $$c$$ and $$d$$ . Point $$O$$ is the center of dilation, and the dilation takes Circle $$c$$ to Circle $$d$$ . Plot a point on Circle $$c$$ . Label the point $$P$$ . Plot where $$P$$ goes when the dilation is applied and label the point $$P'$$ .

Draw

Here are Circles $$c$$ and $$d$$ . Point $$O$$ is the center of dilation, and the dilation takes Circle $$c$$ to Circle $$d$$ . Plot a point on Circle $$d$$ . Label the point $$Q'$$ . Plot the point that the dilation takes to $$Q'$$ and label it $$Q$$ .

Draw

Dilate each vertex of triangle $$ABC$$ using $$P$$ as the center of dilation and a scale factor of 2. Draw the triangle connecting the 3 new points.

Draw

Dilate each vertex of triangle $$ABC$$ using $$P$$ as the center of dilation and a scale factor of $$\frac 1 2$$ . Draw the triangle connecting the 3 new points.

Multiple Choice

What do you notice about the longest side of each of the 3 triangles?

• The longest side is opposite the smallest angle.
• The longest side of each triangle is opposite the largest angle.
• The longest side is always the base of the triangle.
• The longest side is the one with the greatest length.

Multiple Choice

What do you notice about the sum of the angles in each triangle?

• The sum of the angles in each triangle is 180 degrees.
• The sum of the angles in each triangle is 360 degrees.
• The sum of the angles in each triangle is 90 degrees.
• The sum of the angles in each triangle varies based on the triangle type.